Must Solve Q51 level GMAT Question | GMAT Permutation Combination | GMAT Coordinate Geometry

GMAT Preparation Online | GMAT Permutation Combination | GMAT Coordinate Geometry | GMAT Sample Questions

This 700 level GMAT problem is a must solve GMAT quant question. It combines concepts from permutation combination and coordinate geometry.

Question
Rectangle ABCD is constructed in the xy-plane so that sides AB and CD are parallel to the x-axis. Both the x and y coordinates of all four vertices of the rectangle are integers. How many rectangles can be constructed if x and y coordinates satisfy the inequality that x greater than 11 and lesser than 29 and y greater than or equal to 5 and lesser than or equal to 13?

A. 153
B. 153C4
C. 4896
D. 2448
E. 5508

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[sayanbjee]

If there are 4896 rectangles, there should be 4896 right angled triangles with AB parallel to x-axis and B as the right angle. Reasoning is every rectangle will have 4 right angled triangles (so total 19584 right angled triangles); each with A, B, C and D as right angled. Since, the question asks for only B as right angled, the answer would be 4896.

[trinchellinmcmahonn]

Isn't the rectangle you drew @2:37 a square? Are we not required to eliminate possibilities where the sides are of equal lengths, since the question specifically asks for number of possible rectangles?

[praveentk]

Awesome question and answer explanation!

[ishanshah]

The triangle answer is simple if you already have calculated the number of rectangles. You can make 4 right-angle triangles from a rectangle, so to find the maximum number of triangles just multiply the number of rectangles by 4. So 4896 X 4 = 19584 triangles.

[TravisGallagher-vptg]

I have never seen the C sub n notation before - what does it mean?

[toffetjoseph]

For the rectangle question, wouldn't the number of ways to select 2 lines parallel to x-axis be 9*8 instead of 9C2 i.e. 9 points to select from and then one of the remaining 8 ?

[kashyapsushil]

for the variants questions, Q1 - i am not sure how the counting is different for square as there will be 2 vertical and 2 horizontal lines. so could you please let me know where i am going wrong here.
Q2 - i think it should 17c1 and 9c2.

[divyaap]

Answer for traingle question is
9c1*17c1*63

[arijitchakraborty]

492 sqaures. Pattern will be 1*9+2*10+3*11+....upto8*16

[yashharbhajanka]

is the ans for triangle question is 9792